How did China prove Pythagorean Theorem in ancient times?

In 1 1 century BC, Shang Gao, a mathematician in the Zhou Dynasty, put forward "Gou San, Gu Si and Xian Wu". A dialogue between Shang Gao and Duke Zhou was recorded in The Book of Balance Calculation in Zhou Dynasty. Shang Gao said: "... so fold the moment, tick three, fix four, and cross the corner five." Meaning: When two right-angled sides of a right-angled triangle are 3 (hook) and 4 (chord) respectively, the radius angle (chord) is 5. In the future, people will simply say that this fact is "three strands, four chords and five". According to this allusion, Pythagorean theorem is called quotient height theorem.

In the 3rd century A.D., Zhao ·suan in the Three Kingdoms period made a detailed annotation on Pythagorean Theorem in The Book of Changes, which was recorded in Nine Chapters of Arithmetic. Pythagorean theorem was proved in detail by Zhao Shuang's creation of Pythagorean square diagram. Later, Liu Hui also proved the Pythagorean theorem in Liu Hui's notes.

In the 6th century BC, the Pythagorean school of ancient Greece first proposed and proved this theorem in the west. He proved by deduction that the square of the hypotenuse of a right triangle is equal to the sum of the squares of two right angles. So in the west, Pythagorean theorem is called Pythagorean theorem.

The name of Pythagorean Theorem was once Pythagorean Theorem in China, which was translated with the introduction of western mathematics. In 1950s, there was a discussion about the naming of this theorem in academic circles. Finally, Pythagorean theorem is used, which has been widely recognized by educational and academic circles.

1993, the National Committee for Examination and Approval of Natural Science Terminology published mathematical terms, and determined that the Chinese name of the theorem was Pythagoras Theorem, and its corresponding English name was Pythagoras Theorem. The annotation says: "Also known as Pythagoras theorem. The name' quotient height theorem' was used. " At this point, "Pythagorean Theorem" became the standard name established by China.

Extended data:

I. Definition

In a right-angled triangle on the plane, the square of the length of two right-angled sides adds up to the square of the length of the hypotenuse. What are the lengths of the two right sides of a right triangle? And then what? What is the length of the hypotenuse? , then it can be expressed in mathematical language:

Pythagorean theorem is a special case of cosine theorem.

Second, the significance

1. The proof of Pythagorean theorem is the beginning of proving geometry; ?

2. Pythagorean theorem is the first theorem in history that connects numbers with shapes, that is, the first theorem that connects geometry with algebra; ?

3. Pythagorean theorem led to the discovery of irrational numbers and the first mathematical crisis, which greatly deepened people's understanding of logarithms;

4. Pythagorean theorem is the first indefinite equation in history to give a complete solution, which leads to Fermat's last theorem;

Pythagorean theorem is the basic theorem of Euclidean geometry and has great practical value. This theorem is not only a dazzling pearl in geometry, but also widely used in advanced mathematics and other scientific fields.

1971May 15, Nicaragua issued a set of stamps entitled "Ten Mathematical Formulas for Changing the World". These ten mathematical formulas are all selected by famous mathematicians, and Pythagorean theorem is the first one.

References:

Baidu encyclopedia-Pythagorean theorem